Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

`"dy"/"dx" + y` = 5 is a differential equation of the type `"dy"/"dx" + "P"y` = Q but it can be solved using variable separable method also.

`lim_("h" -> 0) (1/("h"^2 sqrt(8 + "h")) - 1/(2"h"))` is equal to ____________.

`lim_("x" -> -3) sqrt("x"^2 + 7 - 4)/("x" + 3)` is equal to ____________.

`lim_("x"-> 0) ("cosec x - cot x")/"x"`  is equal to ____________.

If f : R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x² + 7, then the value of x for which f(g(x)) = 25 is ____________.

`("d"y)/("d"x) + y/(xlogx) = 1/x` is an equation of the type ______.

Integrating factor of the differential equation of the form `("d"x)/("d"y) + "P"_1x = "Q"_1` is given by `"e"^(int P_1dy)`.

Solution of the differential equation of the type `("d"x)/("d"y) + "p"_1x = "Q"_1` is given by x.I.F. = `("I"."F") xx "Q"_1"d"y`.

Correct substitution for the solution of the differential equation of the type `("d"y)/("d"x) = "f"(x, y)`, where f(x, y) is a homogeneous function of zero degree is y = vx.

Correct substitution for the solution of the differential equation of the type `("d"x)/("d"y) = "g"(x, y)` where g(x, y) is a homogeneous function of the degree zero is x = vy.

Let f : R → R be given by f(x) = tan x. Then f^-1(1) is ____________.

If f : `(1, infty) → (2, infty)  "is given by f"("x") = "x" + 1/"x"`, then f^-1 equals to ____________.

Let f(x) = x² – x + 1, x ≥ `1/2`, then the solution of the equation f(x) = f^-1(x) is ____________.

If A and B are symmetric matrices of the same order, then ____________.

If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.

If A is any square matrix, then which of the following is skew-symmetric?

If A `= [(6,8,5),(4,2,3),(9,7,1)]` is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is ____________.

If `vec"a", vec"b", vec"c"` are three vectors such that `vec"a" + vec"b" + vec"a" = vec0` and `|vec"a"|` = 2, `|vec"b"|` = 3, `|vec"c"|` = 5, then value of `vec"a"*vec"b" + vec"b"*vec"c" + vec"c"*vec"a"` is ______.

If `|vec"a"| = |vec"b"|`, then necessarily it implies `vec"a" = +- vec"b"`.

Find the shortest distance between the lines given by `vec"r" = (8 + 3lambdahat"i" - (9 + 16lambda)hat"j" + (10 + 7lambda)hat"k"` and `vec"r" = 15hat"i" + 29hat"j" + 5hat"k" + mu(3hat"i" + 8hat"j" - 5hat"k")`